Buy-in for the mininum or maximum?

You sit down at the 2-5 No-Limit table. The buy-in is $200 minimum, and $500 maximum. What should you buy in for? Does it make any difference?

For a long time I thought that buying in for the max was the best choice, as this gives you an opportunity to put the most money into a hand when you hold the nuts. It makes sense. But lets look at this from another perspective.

Hypothetical situation: let's say you are heads up, you have $200 and the other guy has $800 (or more.) You both go all-in BLIND 2 hands in a row. Who comes out ahead on average?

Here are the 3 possible outcomes:

You lose the first hand, game over. He profits $200.

You win the first hand, lose the second. Game over, he profits $200.

You win the first and second hand. You profit $600.

Even though you only win 1 of 3 situations, the amount you make is $200 more than the other guy's winnings combined.

This observation alone makes a clear choice that there is an advantage to buying in short. A good strategy (online or live play) is to buy in for the minimum, and stand up and leave as soon as you double up your bankroll. There is no sense in gambling your winnings back, just leave and buy-in short again later (live), or on another table (online.)